#FSRS-6

FSRS-6 has 21 trainable weights, including a trainable forgetting-curve decay and a same-day stability term.

See the Model overview for the shared symbols and Model contract.

#Forgetting curve and interval

With the positive decay magnitude $d = w_{20}$, choose $F$ so that $R(S, S) = 0.9$:

$$F=0.9^{-1/d}-1,\qquad
R(t,S)=\left(1+F\frac{t}{S}\right)^{-d}$$

$$I(r,S)=\frac{S}{F}\left(r^{-1/d}-1\right)$$

nextInterval rounds the result to whole days and returns at least one day.

#Initial memory

$$S_0(G)=\operatorname{clamp}\left(w_{G-1},S_{min},S_{max}\right)$$

$$D_0(G)=w_4-e^{w_5(G-1)}+1,\qquad
D_{initial}=\operatorname{clamp}\left(D_0(G),1,10\right)$$

#Difficulty

$$\Delta D=-w_6(G-3),\qquad
D^*=D+\Delta D\frac{10-D}{9}$$

$$D'=\operatorname{clamp}\left(w_7D_0(4)+(1-w_7)D^*,1,10\right)$$

#Stability after review

For $t > 0$, or when enableShortTerm is disabled, the rating selects the following branch.

The update uses the pre-review $D$ and $S$. $H_G = w_{15}$ for Hard and $1$ otherwise; $E_G = w_{16}$ for Easy and $1$ otherwise.

When enableShortTerm is enabled, $C$ is the previous stability multiplied by $\exp(-w_{17}w_{18})$; otherwise, $C = S$:

$$S_f=\min\left(w_{11}D^{-w_{12}}\left((S+1)^{w_{13}}-1\right)e^{w_{14}(1-R)},C\right)$$

$$S_r=S\left[1+e^{w_8}(11-D)S^{-w_9}\left(e^{w_{10}(1-R)}-1\right)H_GE_G\right]$$

$$S'_{raw}(G)=
\begin{cases}
S_f,&G=1\\
S_r,&G\in\{2,3,4\}
\end{cases}$$

$C$ is an implementation cap for post-lapse stability, not a separately configured stability floor. The model then clamps $S'_{\mathrm{raw}}$ to the range from $S_{\min}$ to $S_{\max}$.

#Same-day update

Here, “same-day” means the model receives elapsedDays = 0; the model does not inspect calendar dates. Direct callers and the scheduler’s chrono determine the elapsed value.

When enableShortTerm is enabled and $t = 0$:

$$s_{inc}=S^{-w_{19}}e^{w_{17}(G-3+w_{18})}$$

$$S'=\operatorname{clamp}\left(Sm,S_{min},S_{max}\right),
\qquad
m=\begin{cases}
s_{inc},&G=1\\
\max(s_{inc},1),&G\ge2
\end{cases}$$

Hard, Good, and Easy cannot reduce stability below its current value; Again may reduce it.